Suppose that f(x) is a function with f(105)=25 and
f '(105)=4. Estimate f(106).
Not sure how to go about this problem..

Question

Suppose that f(x) is a function with f(105)=25 and 
f '(105)=4. Estimate f(106).
Not sure how to go about this problem..

freckles · Answer

$$y-f(a)=f'(a)(x-a) \ y=f'(a)(x-a)+f(a) $$

freckles · Answer

$$f(x) \approx f'(a)(x-a)+f(a) \text{ for values of x near a }$$

freckles · Answer

Hello? Do you know what the above is?
The first line is point slope form of the tangent line of f at (a,f(a))
The second line is the same equation I just added f(a) on both sides.
I'm using it as a linear approximation for numbers x near a

anonymous · Answer

hello! I'm sorry for the late reply, my computer crashed due to a failed update yesterday. But yes I understand this now, thank you so much for your help!

freckles · Answer

np

freckles · Answer

so you know your a is 105 in this case?

freckles · Answer

$$f(x) \approx f'(105)(x-105)+f(105) \text{ for values of x near a }$$